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Direct Measurement of the Free Energy of Aging Hard-Sphere Colloidal Glasses

The nature of the glass transition is one of the most important unsolved problems in condensed matter physics. The difference between glasses and liquids is believed to be caused by very large free energy barriers for particle rearrangements; however so far it has not been possible to confirm this experimentally. We provide the first quantitative determination of the free energy for an aging hard-sphere colloidal glass. The determination of the free energy allows for a number of new insights in the glass transition, notably the quantification of the strong spatial and temporal heterogeneity in the free energy. A study of the local minima of the free energy reveals that the observed variations are directly related to the rearrangements of the particles. Our main finding is that the probability of particle rearrangements shows a power law dependence on the free energy changes associated with the rearrangements, similarly to the Gutenberg-Richter law in seismology.